WASHINGTON — The Trump administration has decided that it needs no new legal authority from Congress to indefinitely keep American military forces deployed in Syria and Iraq, even in territory that has been cleared of Islamic State fighters, according to Pentagon and State Department officials.

In a pair of letters, the officials illuminated the Trump administration’s planning for an open-ended mission of forces in Syria beyond the Islamic State fight. Secretary of State Rex W. Tillerson foreshadowed the plan in a speech last month, saying that troops will stay in Syria to curb Iran and prevent the Syrian government from reconquering rebel-held areas.

Though Mr. Tillerson also cited a need to mop up the remnants of the Islamic State and keep from leaving a vacuum in which the group could regenerate, other administration officials put far greater emphasis on the extremists. In the letters, they said that the continued potential threat from the Islamic State provided a legal rationale for the Trump administration to keep American troops deployed there indefinitely.

“Just as when we previously removed U.S. forces prematurely, the group will look to exploit any abatement in pressure to regenerate capabilities and reestablish local control of territory,” wrote David Trachtenberg, the deputy undersecretary of defense for policy.

About 2,000 American troops are in Syria, where nearly all the territory once held by the Islamic State has now been liberated. Mr. Tillerson deemed the group “substantially, but not completely defeated,” warning that the insurgents remained a threat.

Mr. Trachtenberg wrote the letter to Senator Tim Kaine, Democrat of Virginia, who had asked the Trump administration to explain its understanding of its authority to stay on in Syria. The State Department sent him a similar letter, which also argued that international law provided a basis for American forces to remain in Syria — despite the lack of consent from the Syrian government — to protect Iraq and the United States from terrorists.

And both letters said American troops may strike at Syrian government or Iranian forces deemed to threaten Americans or Syrian rebel groups that are assisting the United States in fighting the Islamic State, also known as ISIS.

“The United States does not seek to fight the government of Syria or Iran or Iranian-supported groups in Iraq or Syria,” wrote Mary K. Waters, the assistant secretary of state for legislative affairs. “However, the United States will not hesitate to use necessary and proportionate force to defend U.S., coalition, or partner forces engaged in operations to defeat ISIS and degrade Al Qaeda.”

American troops carried out strikes against forces loyal to President Bashar Assad of Syria several times in 2017 in the name of defending American-supported rebel groups.

Especially as a matter of international law, the administration’s theory for why the United States will have authority to keep carrying out such operations indefinitely amounts to “a tenuous legal justification atop of another tenuous legal justification,” said Jack Goldsmith, a Harvard Law School professor and former Justice Department lawyer in the Bush administration.

And in a statement addressing domestic law, Mr. Kaine said the executive branch was stretching its interpretation of its war authority too far. He called on the administration to seek new authorization for any continued, long-term mission in Syria and Iraq — especially “to strike pro-Assad forces in areas devoid of ISIS to protect our Syrian partners who seek Assad’s overthrow.”

He also criticized the basis on which the administration ordered strikes on a Syrian government air base last April as punishment for using chemical weapons. At the time, President Trump claimed powers as commander-in-chief to issue the strikes rather than on any theory of congressional authorization.

The senator accused Mr. Trump of “acting like a king by unilaterally starting a war.”

The executive branch’s core legal theory that it is authorized by Congress to fight the Islamic State in both Iraq and Syria was first put forward by the Obama administration in 2014, when ISIS swept out of Syria and began rapidly conquering portions of Iraq. The United States started bombing Islamic State forces to curb their advances.

Under both Mr. Obama and Mr. Trump, the executive branch has argued that the war against the Islamic State is covered by a 2001 law authorizing the use of military force against the perpetrators of the Sept. 11 attacks and a 2002 law authorizing the invasion of Iraq.

That theory is disputed. While ISIS grew out of an offshoot of Al Qaeda, the two groups by 2014 had split and became warring rivals. Before the rise of ISIS, the Obama administration had deemed the Iraq war over and largely withdrawn American troops.

Still, Congress has continued to appropriate funds for the operations, even as it has failed to enact any new or updated war authorization that specifically addresses ISIS. No court has addressed the question of whether the executive branch has legitimate authority from Congress to battle the Islamic State.

A version of this article appears in print on , on Page A8 of the New York edition with the headline: Administration Says Syria Forces Don’t Need New Approval. Order Reprints | Today’s Paper | Subscribe